Energy storage modeling and control

ABSTRACT

Systems and methods for optimal planning and real-time control of energy storage systems for multiple simultaneous applications are provided. Energy storage applications can be analyzed for relevant metrics such as profitability and impact on the functionality of the electric grid, subject to system-wide and energy storage hardware constraints. The optimal amount of storage capacity and the optimal operating strategy can then be derived for each application and be prioritized according to a dispatch stack, which can be statically or dynamically updated according to data forecasts. Embodiments can consist of both planning tools and real-time control algorithms.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/205,495, filed on Nov. 30, 2018, which is a continuation of U.S.patent application Ser. No. 15/069,530, filed on Mar. 14, 2016, which isa continuation of U.S. patent application Ser. No. 13/838,014, filed onMar. 15, 2013 and issued as U.S. Pat. No. 9,509,176 on Nov. 29, 2016,which claims priority to and the benefit of U.S. Provisional PatentApplication No. 61/620,206, filed on Apr. 4, 2012, all of which areincorporated by reference herein in their entirety.

BACKGROUND

It is generally recognized that the installation and use of an energystorage system (an “ESS”) on an electrical grid can result in materialbenefits (operational, financial, environmental, etc.) to gridparticipants and/or stakeholders, and by doing so can generate materialfinancial returns to an entity owning or controlling the energy storageassets. Energy storage techniques can generate these kinds of benefitsthrough a range of potential applications (“ES applications”), such as(i) the provision of certain ancillary services for which there areestablished energy or capacity market mechanisms (e.g. frequencyregulation, spinning reserves, black start capacity), (ii) load Shiftingor peak shaving, (iii) deferral or avoidance of otherwise necessarytransmission or distribution upgrades, (iv) relief of transmission ordistribution bottlenecks or other constraints, (v) integration ofintermittent renewable generation, whether through smoothing, rampingservices, the provision of shaped power or otherwise, (vi) hybridizationof generation assets to increase fuel efficiency or reduce carbonemissions, (vii) provision of backup power or uninterruptable powersystem (“UPS”) during islanded operation, (viii) time shifting of energypurchases and sales for cost saving or arbitrage purposes, (ix)provision (or committed availability to provide) various operatingreserves, and (x) provision of power, energy or services that mightotherwise be provided by a natural gas peaking plant or other powergeneration sources. The foregoing is intended to be a representativelisting of ES applications, and not an exhaustive listing. In many casesa single ESS installed in a specific location can provide multiple ESapplications (sometimes referred to as the stacking of applications). Asused herein, references to a single ES application may include acombination or stacking of multiple ES applications.

The existence and extent of the benefits and/or related financialreturns from a specific installation and use of an ESS can be dependenton a broad range of factors. These factors include the cost of the ESS(which is generally measured in terms of $/kW and/or $/kWh), the ESS'sratio of power to energy, the size of the ESS (in kW or kWh), the roundtrip efficiency of the ESS, the cycle life and/or useful life of theESS, the manner in which acquisition of the ESS is financed, the siteand installation costs of the ESS, the ongoing operating and maintenancecosts of the ESS. Additional factors can also relate to the location ofthe ESS installation and the ES application(s) for which it is used.These factors can include energy prices and other market conditions, thespecific grid conditions giving rise to a need for the ES application,the pricing/compensation/tariffs or other incentives available for theproduct or service provided by the ES application, the reliability offorecasts of available power, and the mix of generation assets servingthe geographic (or the collection of electrical connections to an ESS)area that includes the ESS.

A number of studies and simple models exist which each provide a degreeof guidance regarding potential ES applications, the basic types of ESStechnologies that may be appropriate for the ES applications, potentialmarket sizes, and maximum ESS costs for the use of an ESS to beeconomical. These studies and models can be useful in providing overallinsight into future markets and the appropriateness of current or futureenergy storage technologies to address certain needs or opportunities onthe grid. The studies, however, do not provide specific insight as tothe appropriate specifications for an ESS providing a particular ESapplication at a particular location. Likewise, the studies do notprovide specific insight into exactly how such ESS would be operated andused for the ES application at such location. Furthermore they do notcouple operating mode to the economic metrics that inform the optimalappropriate energy and power characteristics of an ESS purchase.

In the absence of these insights, the existing studies and models areineffective with respect to demonstrating whether or not installationand use of an appropriate ESS in a particular location to perform aparticular ES application will, if operated in an appropriate manner, beattractive or even feasible from a financial perspective. Given that theexisting studies and models are ineffective in this way they are notuseful as a planning tool for grid participants, planners or regulators.In this sense there is a gap in the analytic tools available withrespect to energy storage for the grid.

SUMMARY

Embodiments of the disclosed subject matter can relate to a generalmethodology for optimal planning of energy storage assets for fulfillingsimultaneous applications. Embodiments of the disclosed subject mattercan also relate to real-time control algorithms that can implement thegeneral methodology to manage energy storage assets fulfillingsimultaneous applications in a way that maximizes asset revenues andprofitability.

In general, in an aspect, embodiments of the disclosed subject mattercan provide a tangible computer readable medium encoded withcomputer-executable instructions that, when executed by a computer oranother operation agent, cause the computer to receive input parametersincluding historical data relating to factors that influence theoperation of an energy storage system, a physical model of the energystorage system, a physical model of other systems to which the energystorage system is connected, pricing information relating to possiblerevenue from the energy storage system, a possible energy storage systemconfiguration, a possible energy storage system operating strategy, anenergy-supply forecast, and an energy storage system cost model, andcalculate an optimal energy storage system operating strategy using theinput parameters, output an optimal energy storage system capacity andspecification based on the calculated energy storage system operatingstrategy, and execute the energy storage system operating strategy in areal-time control system.

Embodiments of the disclosed subject matter can include a number ofmodeling applications, which allow a user to input (i) historic orprojected data regarding operating and market conditions at a specificlocation over a period of time, (ii) specific data on the ES applicationand the needs/opportunities to be addressed by the ES application,including specific information on tariff schemes and/or other financialincentives, (iii) specifications and operating characteristics for anESS that will provide this ES application at that location, andenergy-supply forecasts. In some embodiments, the modeling applicationsare highly sophisticated, the historic or projected data is highlygranular, and the specifications and/or operating characteristics can behighly complete or full, but such characteristics are not required.Embodiments of the disclosed subject matter can also demonstrate theoperation of the ESS on a concurrent basis over the course of the timeperiod for which an ESS is available to the grid (e.g. specifyingwhether at any given moment the ESS is charging or discharging, and atwhat rate, or doing neither) and can calculate, or predict, thefinancial results of the installation of this ESS and this operation ofit. Embodiments of the disclosed subject matter can also engage invarious optimization exercises using its ability to demonstratemoment-to-moment ESS operation, and the related financial results. Itshould be noted that embodiments of the present disclosed subject mattercan equally apply to a large number of ESS technologies such aselectrochemical batteries, electrical capacitors, superconductingmagnetic rings, mechanical flywheels, compressed air energy storage(CAGS), hydrostatic, etc. Embodiments can also treat a portfolio of ESSassets.

An example of an optimization exercise is a strategy for operating anESS. Underlying the operation of the ESS for a specific ES applicationis an operating strategy (an “ES operating strategy”) that seeks to usethe ESS to provide an ES application in manner that is cost efficientand operationally effective. It can be such as an ES operating strategythat determines the activity of the ESS (e.g., charging, discharging orneither) at each given moment. Embodiments of the disclosed subjectmatter can allow for an ES operating strategy to be input, and/or canprovide for an ES operating strategy to be derived and refined. Such anoptimal ES operating strategy can be found from the examination of largesets of scenarios and results reflecting minor alterations of a given ESoperating strategy with help of well-known mathematical instruments,such as Monte Carlo optimization and machine learning techniques.

Another example of an optimization exercise is the specifications of theESS. These specifications can relate to the characteristics of theenergy storage provided by the ESS (e.g., a ratio of power to energy,round trip efficiency, cycle and calendar life, maintenancerequirements, etc.) and the quantity of energy storage provided by theESS. The operational and financial benefits that can be generated by anESS, and the costs of installing and operating an ESS, can be a functionof both the characteristics and the quantity of the energy storageprovided by the ESS. Embodiments of the disclosed subject matter canderive optimal ESS characteristics and quantity by examining the totaland marginal cost of these and the total and marginal operational andfinancial benefits generated by ESS, in each case based uponinstallation and operation the ESS to provide a specific ES applicationat a specific location in accordance with a specific ES operatingstrategy. Changes with respect to the ES application, the installationlocation (and any related conditions), and/or the ES operating strategycan result in changes to the optimal characteristics and/or quantity ofthe energy storage of the ESS.

Many of the factors/inputs relevant to the calculations, demonstrationsand optimizations provided by certain embodiments of the disclosedsubject matter can be highly variable over long time frames and/or oververy short time frames, and in any event are typically uncertain. Thesecan include factors/inputs such as wholesale energy prices, natural gasprices, ancillary services prices, loads, and weather conditionseffecting loads, energy output from wind farms or solar plants, interestrates and other factors impacting financing costs, etc. Embodiments ofthe disclosed subject matter can demonstrate operation of an ESS withall control decisions being made without the benefit of any data thatwould be unknown or uncertain if these control decisions were being madein real time. Each ES operating strategy can be developed, tested andrefined on this basis, primarily using means such as statisticalcalculations, Monte Carlo analysis and machine learning techniques.Embodiments of the disclosed subject matter can assume tolerance levelsfor non-performance by the ESS with respect to ES applications giventhat the control decisions generated can be based on probabilitiesrather than certainties. Embodiments of the disclosed subject matter canmeasure and take into account the costs of such non-performance, and canalso allow for adjustment the tolerance of non-performance. Embodimentscan allow for periodic or concurrent operating algorithm improvementsbased on historical information derived from in-use behavior of ESScontrol strategies, changes in the grid connectivity, demand, and theavailability of new power sources.

Assuming the use of adequate data processing hardware, embodiments ofthe disclosed subject matter can make calculations and can generatecontrol decisions in real time, e.g., at a speed such that the ESS canbe controlled using data generated and input on an ongoing basis rightup until the point immediately prior to the generation of the controldecision. The process of acquiring data and other inputs and generatingcontrol decisions can occur continuously, in intervals that are, forexample, as short as the shortest interval in the acquired data. Thus,for example, if a controller is determining a control decision in parton the basis of a load measured and delivered in 30 second intervals (inaddition to many other inputs and factors), then the controller cangenerate control decisions in increments 30 seconds to one hour,immediately upon the receipt of the 30 second load data. Embodiments ofthe disclosed subject matter can also demonstrate how an arbitrarynumber of simultaneous ES applications can be addressed with dynamic,real-time scheduling. Longer term future strategies that are dynamicallyupdated at shorter intervals.

Embodiments of the disclosed subject matter can have several differentpotential uses. For example, the techniques described herein can be usedby prospective purchases/users of energy storage to evaluate whether andwhere an installation and use of energy storage will be financiallyattractive. The techniques can also be used to test and demonstrate theimpact that such an installation and use will have on grid conditionsand/or grid stability, which would be of use to system operators and/orothers responsible for grid stability. In each case the techniques maybe used to do so on the basis of optimal operation of an ESS that isoptimal in terms of its characteristics and quantity (or, if desired, ofan ESS having other specified characteristics and quantity). Embodimentsof the disclosed subject matter may, with respect to any of theforegoing, demonstrate and calculate how results or outcomes wouldchange with changes to key inputs, such as changes to the cost ofenergy, energy storage or ancillary services, or changes to relevantregulatory or market structures, or changes in generation and/or loadcharacteristics. Embodiments of the disclosed subject matter can also beused by developers of energy storage and ESS's to determine the set ofESS characteristics that will be most valuable and effective for a givenES application. The disclosed subject matter should be useful forregulators and/or system operators to evaluate whether and how changesto tariffs, energy or capacity markets, or regulations will impact theinstallation and use of energy storage to address specific grid issuesor challenges. In addition, embodiments can utilize extant ESS to informeconomic and operational decisions regarding the purchase and impact ofadditional energy-generation resources or additional ESSs.

Embodiments of the disclosed subject matter can also serve as acontroller incorporated into an ESS or installed in connection with anESS which can dispatch the ESS, e.g., on a moment-to-moment basis inreal time, allocating storage capacity across available applications anddirecting the ESS to charge or discharge, and at what rates; or to beheld in abeyance for future sources of energy or storage of excessenergy. The manner in which the ESS is controlled can be adjusted basedon, for example, desired financial or other outcomes, and/or to reflectchanges in relevant rules or conditions. The controller can dispatch theESS on the basis of operating and market data provided to the controlleron a real time basis.

These and other capabilities of the disclosed subject matter, along withthe invention itself, will be more fully understood after a review ofthe following figures, detailed description, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The description below refers to the accompanying drawings, of which:

FIG. 1 is an exemplary schematic of an ES application optimization tool.

FIG. 2 is an exemplary schematic of one embodiment of an ES applicationoptimization tool for wind power regulation.

FIG. 3 is the mathematical formulation of one embodiment of an operationstrategy for wind power regulation.

FIG. 4 illustrates an exemplary result of operating an ideal ESS forsmoothing wind power variability into one-hour blocks. A system operatorcan incentivize the commitment and delivery of constant power in a giventime interval.

FIG. 5 shows an exemplary graphical interface of the wind powerregulation optimization tool showing an embodiment of delivered powershaping produced with a battery with a given energy capacity and maximumcharge and discharge rate. In this example a dynamic charging strategyis employed.

FIG. 6 shows an example of optimization of ESS capacity for wind powerregulation. In this example, the optimal ESS capacity is found wheremarginal revenues equal marginal cost for a battery of given power toenergy ratio.

FIG. 7 shows an example of optimization of ESS characteristics for windpower regulation. In this example embodiment, optimization is performedcomparing batteries of different power to energy ratios and optimalcapacities, holding all other characteristics, such as pricing strategyand incentive fixed. In other embodiments, all variables are subject tooptimization.

FIG. 8 is an exemplary schematic of one embodiment of an ES applicationoptimization tool for supplying an optimal combination of an ESS andbalancing reserves in support of uncertain renewable generation.

FIG. 9 illustrates an exemplary result of operating an ESS in concertwith conventional reserves to provide balancing requirements in supportof uncertain renewable generation.

FIG. 10 illustrates an exemplary power shaping strategy applied to arenewable generation time trace to determine power block commitments.

FIG. 11 illustrates alternative exemplary power shaping strategiesapplied to a renewable generation time trace to determine power blockcommitments.

FIG. 12 illustrates an exemplary power shaping strategy applied to arenewable generation time trace with slope inversion constraints.

FIG. 13 shows an exemplary embodiment of the graphical interface of therenewable generation balancing tool.

FIG. 14 is an exemplary schematic of one embodiment of an ES applicationoptimization tool for power arbitrage.

FIG. 15 illustratively shows one example of the buy-sell pruningalgorithm according to one embodiment of the ES application optimizationtool for power arbitrage.

FIG. 16 is an exemplary schematic of one embodiment of an ES applicationoptimization tool for peak load shaving and transformer overloadprotection.

FIG. 17 shows an exemplary operation of real time control in oneillustrative example where ESS capacity is optimally allocated in orderto mitigate multiple load peaks in a 48-hour time horizon.

FIG. 18 illustrates an exemplary result of operating a set of ESS ofdifferent sizes and in an optimal manner for shaving a sinusoidal peakload.

FIG. 19 shows an exemplary embodiment of the graphical interface of thepeak load shaving and transformer overload protection optimization tool.

FIG. 20 is an exemplary schematic of one embodiment of an ES applicationoptimization tool or minimizing energy cost in a micro-gridinstallation.

FIG. 21 shows an exemplary operation of real time control in oneillustrative example where ESS capacity is optimally allocated in orderto minimize energy cost in a micro-grid installation.

FIG. 22 shows an exemplary embodiment of the graphical interface of themicro-grid optimization tool.

FIG. 23 is an exemplary representation of the dispatch stack ofsimultaneous ES applications.

FIGS. 24A and 24B are exemplary schematics of one embodiment ofReal-time Dispatch and Control of Simultaneous ES applications.

FIG. 25 illustrates an exemplary equivalence of centralized anddistributed storage.

DETAILED DESCRIPTION

Embodiments of the disclosed subject matter can provide techniques forproviding an ES application optimization tool that includes a set ofmodeling tools implementing a general methodology for determining theoptimal ESS capacity and characteristics where the financial worth orother combinations of figures of merit of the ESS asset is maximized.For example, the tool can solve for the point (e.g., batterycharacteristics and operating strategy) where marginal cost equalsmarginal revenues for a specific ES application as a function of ESScapacity or characteristics. The resulting ESS capacity is the optimalcapacity to allocate to the ES application. Embodiments of the disclosedsubject matter can also provide real-time control algorithms that canmanage energy storage assets fulfilling simultaneous applications in away that maximizes asset revenues and profitability. Other embodimentsare within the scope of the invention.

FIG. 1 shows the general components of ES application optimization tool11, although the ES application optimization tool 11 can include more orfewer components. Historical data 13 can relate to quantifiable factorsthat can have an effect on the overall operation of an energy storagesystem, such as market data, weather data and forecasts, econometricindicators, calendars etc. Historical data 13 can be obtained fromproprietary sources, such as data acquisition systems connected torenewable generation assets and from public sources such as independentsystem operators databases. Physical models of ES application 14 canrelate to the mathematical model of ES application, both pertaining toESS, such as chemical, electrical, mechanical and thermodynamicequations, and pertaining to other components, such as chemical,electrical, mechanical and thermodynamic equations of power equipment.Physical models of ES application 14 can be obtained from specializedliterature, such as scientific journals and engineering textbooks, aswell as from proprietary sources, such as user manuals. Revenuemechanisms 15 can relate to revenue opportunities captured by deployingESS for ES applications such as ancillary services, price arbitrage,peak shaving, voltage regulation, etc. Possible ESS configurations 16can relate to ESS capacity, power rating, charge and discharge rates,useful life, efficiency losses, etc. Revenue mechanisms 15 can beobtained from publicly available documentation on regulatedtariff/penalty schemes in power markets as well as from proprietarymodels involving, by means of example, power trades.

Possible ESS operating strategies 17 can relate to dispatch rulescomplying with external as well as internal conditions and aiming atmaximizing ESS operating life and financial worth. Possible ESSoperating strategies 17 can be obtained from ESS hardwarespecifications. By way of example, possible ESS operating strategies canregulate when the ESS is discharged and charged in response to exogenousinputs and endogenous ESS conditions. ESS operating strategies can alsoimpose constraints such as the extent to which ESS available capacity isperused during charging and discharging or the rate of charging anddischarging. ESS cost model 18 can refer to proprietary cost modelsrelating ESS capacity and characteristics to capital and operating costof the ESS asset. ESS cost model 18 can be obtained from ESS hardwarespecifications. By way of example, ESS hardware could be specified interms of rated energy, rated power, time duration of charge anddischarge, number of cycles, and the effect of charge and dischargerates on ESS wear, all of which can contribute to the cost of ESShardware.

ES application optimization algorithm 12 can perform a minimal set ofasset simulations converging to the optimal ESS capacity andcharacteristics for the selected application, which are expressed inoutput 19. For example, one output of the tool can consist of theoptimal battery capacity and the financial worth of the same in theselected ES application. ES application optimization algorithm 12 canincorporate the rules and constraints in possible ESS operatingstrategies 17. Thus, for example, the ES application optimizationalgorithm can calculate the correct amount of storage and ESS power andfine tune the operating strategy to achieve a desired amount of storage.

For example, the ES application optimization algorithm 12 can consist ofapplying a specified operation strategy to the operating conditions of aspecific application to produce a financial result for each ESS capacity(MWh) and power (MW) capability. With a matrix of financial resultsspanning a large space of capacity and power characteristics, theoptimum ESS system can be located by visual inspection, regressionfitting to a function with a maximum, or application of other standardmultivariate optimization methods.

By way of example, FIG. 2 illustrates an embodiment in a model thatdemonstrates the operation of an ESS installed for the purposes ofaltering the energy production of a wind farm so as to minimizecosts/penalties resulting from the intermittency of wind power. Thismodel adopts the perspective of a wind farm owner selling on a merchantbasis the energy it produces. This model uses the following inputs,amongst others (although other inputs can be used):

-   -   a. Historical energy production 13-1, in 30 second intervals, of        an actual wind farm over multi-month periods;    -   b. Historical LMP (Locational Marginal Pricing) 13-2 applicable        to that wind farm for the periods covered by the production        data;    -   c. Physical models of ES application 14;    -   d. Pricing/penalty schemes for wind intermittency 15-1 aimed at        internalizing the costs incurred as a result of wind        intermittency, particularly those costs associated with        imbalances between energy scheduled/committed to be provided by        the wind farm to the grid and the energy actually provided by        the wind farm to the grid;    -   e. Premium for wind power shaping 15-2 aimed at creating an        incentive for wind power producer to supply in flat power        blocks, or other time-dependent power feeds;    -   f. Possible ESS configurations 16 relating to ESS capacity,        power rating, charge and discharge rates, useful life,        efficiency losses and other characteristics;    -   g. Possible ESS operating strategy 17 relating to the operating        strategy in conjunction with the wind farm so that the energy        delivered to the grid by the combination of the wind film and        the ESS consists of flat blocks (or power ramps) of energy (e.g.        one hour of constant power, or time-dependent power increase or        decrease) committed to in advance (e.g. 20 minutes in advance of        the hour);    -    ESS cost model 18 relating to a separate proprietary model, and        other relevant information, indicating the relative and absolute        cost of ESS's having different technologically feasible        characteristics with respect to power, energy, cycle life,        footprint, efficiency, etc.)

By way of example, FIG. 3 shows ESS operating strategy 17 in oneembodiment employed for power regulation, which can consist of iteratingthrough each time step, applying constraints and commitments, andcommitting enough power PowerCommitted to the next time block to bringcurrent state of charge SOCCurrent plus forecast incoming powerPowerForecast for the time period back to the desired state of chargeSOCDesired, within time period FlatTime scaled by state of chargeurgency SOCUrgency. For example, suppose that the ESS contains 2 MWh andhas commitments totaling 1 MWh for the next two hours before the nextcommitment. During this period, suppose a total of 0.5 MWh of wind. Soat the beginning of the next commitment period, the ESS is expected tohave 1.5 MWh. If the desired state of charge is 1 MWh and the state ofcharge urgency is 1, the next committed action can be to discharge 0.5MWh during the next block. ESS charging and discharging actions canscale with commitment interval and state of charge urgency, as it willbe apparent to those skilled in the art. Additional parameters caninclude the time prior to commitment. All parameters can be arbitrarilychanged by the user.

The model can also consider the financial impact of the wind farm, orintermittent power supply, operating in conjunction with the ESS, takinginto account the costs/penalties/lost revenues avoided by the powersupplier; the capital cost, useful life and efficiency losses of theESS; and many other factors. For example, the actions of a battery canbe modulated by the cost of battery operation during the simulationbecause the revenue of charge and discharge pair may be less than theamortized cost of owning and operating the ESS, including wear anddepreciation of ESS hardware. Thus, the financial impact can operate asan integral component of ESS operation that is evaluated again at theend of a simulation to indicate the overall financial performance, whichcan be used for optimization and ultimately decision-making.

ES application optimization algorithm 12 can perform a series ofoptimization exercises to indicate the optimum ESS in tennis of powerand energy) an optimum operation of this ESS in conjunction with thewind farm, and the financial results achieved (e.g., outputs 19 in FIG.2). This optimization can be based on balancing the total and marginalcosts of an ESS with the total and marginal revenues/cost savingsrealized through its operation, and in this way takes into account thedecreasing returns to scale of an ESS. The model reflects broad sets ofexogenous assumptions and inputs, but can be structured such that mostof these can be varied to test and demonstrate ESS operations andbenefits under a wide range of conditions.

For example, the model can compute the return on investment (ROI) orother financial metric for each of a set of strategies and ESScharacteristics then choose the best strategy and ESS characteristics toachieve the greatest ROI or other financial metric. The optimum pointcan be located, for example, using list comparison, multivariateregression, local optimization techniques that travel up a localgradient vector, or other numerical optimization method known to thoseskilled in the art.

An exemplary set of outputs 19 can be a graphical and numericalrepresentation of battery performance, a list of financial metricsincluding but not limited to $USD, Internal Rate of Return (“IRR”), netpresent value (“NPV”), and those metrics as a function of batterycapacity, and the strategy used including optimized strategy parameters.

FIG. 4 presents the basic operation of an ESS (with unlimited power andenergy) to convert the energy production of a wind farm (black dots 43in FIG. 4) into flat 1-hour blocks of energy. ESS charge periods 41alternate with ESS discharge periods 42. A system operator canincentivize the commitment and delivery of constant power in a giventime interval; it is therefore desirable to identify the optimalconfiguration of an ESS for wind power regulation.

FIG. 5 shows one embodiment of the graphical interface of the wind powerregulation optimization tool. In this case the behavior of a battery ESSis shown. Panels 51 and 52 set out key inputs regarding (i) thespecification of the relevant ESS, “control knobs” for the strategy tobe used by the ESS, and (iii) the wind energy pricing scheme pursuant towhich the wind farm incurs costs/penalties due to the intermittency ofits energy production. A user, evaluator, or regulatory strategist canindependently vary all of these inputs. Panel 53 presents financialoutputs of the model, e.g., the cost of the specified ESS, the revenuesof the power supplier assuming no ESS, the revenues of the powersupplier, if the specified ESS were operated with the power supplier inaccordance with the strategy specified, and the payback period, IRR andNPV with respect to the investment and operation of the power supplierwith ESS as presented.

Graph 54 presents the energy output of the wind farm (line 55) assumingno ESS, the commitments as to the delivery of flat blocks of power thatthe wind farm with the specified ESS would make (line 56), and theactual energy output of the wind farm with ESS (line 57). Because theESS is limited as to its power and energy, wind power with ESS will notbe able to fulfill all committed deliveries of flat blocks, and in thoseinstances it will fail (referred to here as errors and seen on graph 54as the places where the line 56 is not aligned with line 57). The use ofa wind farm is purely exemplary and for illustration purposes.

Graphs 58 and 59 show the operation of the ESS at each moment to achievethe result Shown in the graph 54. Graph 58 shows the action of the ESSin charging (absorbing power generated by the wind farm) and discharging(adding power to the power generated by the wind farm). Graph 59 showsthe state of charge of the ESS at each moment, e.g., the amount ofenergy stored in the ESS at that moment relative to the full energystorage capacity of the ESS.

FIG. 6 presents an optimization exercise with respect to the quantity ofESS, assuming a fixed power to energy ratio (which may be varied by theuser) and with such optimization being on the basis of marginal costsequaling marginal revenue. Marginal revenues 63, marginal cost 62 andtheir intercept 64 are simultaneously shown in graph 61. The coordinatesof 64 represent the optimal battery capacity for this ES application,delivering an internal rate of return (IRR) of 9% and a battery paybackof 6.4 years. The graph is calculated by finding the revenues and costsfor a set of ESS energy capacities (MWh) with other inputs heldconstant, then using finite differences or regression fits to computeand plot marginal values.

FIG. 7 presents an optimization exercise with respect to ESScharacteristics (e.g., with the optimum quantity of ESS for eachpossible set of ESS characteristics having been determined by the prioroptimization exercise). In this case, optimization is determined byfinding the battery delivering the highest IRR. Table 71 lists numericalresults for batteries of different capacities, energy to power ratios,net present values (NPV), internal rates of return, and ESS cost in$/kWh. Graph 72 is a plot of IRR against energy to power ratios (alsomeasured in hours of battery discharge) and the highest IRR is found tobe 9% for a 3-hour battery (point 73 in FIG. 7).

In all of the interfaces shown, the user can independently vary theinputs shown, whereupon the model recalculates and presents a revisedset of graphs and calculations based on the changed input. Thisrecalculation process can be near instantaneous.

By way of another example, FIG. 8 illustrates an embodiment in a modelthat demonstrates the operation of an ESS installed for the purposes ofminimizing the total cost of balancing renewable energy powerfluctuations with a combination of energy storage and conventionalreserves. Demand and supply for electric power must be balanced at alltimes in a power system. In order for this happen, system operators callgenerators in economic order up to real-time demand. However, because ofthe inherent uncertainty of renewable generators, real-tune availabilitymight differ from the amount that was previously committed. Systemoperators must therefore carry a large amount of reserves to deal withlast minute variations: The dispatch of these reserves goes by the nameof balancing services. The addition and optimal operation of the rightamount of ESS can reduce the total system cost of balancing services.This embodiment of the disclosed subject matter can calculate theoptimal size and specifications of an ESS that is required to shape thepower from a renewable energy generator in such a way that the totalcost of ESS and balancing services is the lowest possible. Thisembodiment can also calculate how the total cost changes as function ofresource forecast uncertainty, shaping requirements, cost of ESS, costof reserves and ESS control strategy, among other things. This model canadopt the perspective of a system planner or system operator who istrying to minimize the cost of incorporating substantial amounts ofrenewable energy generation in the power grid. This model can also usethe following inputs, amongst others:

-   -   a. Historic renewable energy generation 813-1, typically in        intervals of one hour or less, over a desired time period;    -   b. Historical forecast error 813-2, typically in intervals of        one hour or less;    -   c. Physical models 14-1 of ESS, including ESS rate of        degradation as a function of configuration and operating        parameters;    -   d. Forecast uncertainty model 14-2, including time of arrival        error, magnitude error and other statistical description that        will appear evident to those skilled in the art;    -   e. Cost of providing reserves for energy and power 15;    -   f. Possible ESS configurations 16 relating to ESS capacity,        power rating, charge and discharge rates, useful life,        efficiency losses and other characteristics;    -   g. Possible ESS operating strategy 17 relating to the operating        strategy in conjunction with reserves so that balancing costs        are the lowest; and    -   h. ESS cost model 18 relating to a separate proprietary model,        and other relevant information, indicating the relative and        absolute cost of ESS's having different technologically feasible        characteristics (e.g. with respect to power, energy, cycle life,        footprint, efficiency, etc.).

On the basis of the foregoing, the model can calculate the lowest costcombination of ESS and reserves to supply balancing requirements,accounting for user's defined forecast uncertainty, power shapingrequirements and other system constraints.

By way of example, FIG. 9 shows illustrative time traces over a two-dayperiod. Based on wind power forecast 91, a wind farm owner makescommitments to supply power 92. However, real-time wind power 93 happensto deviate from forecast 91 and reserves must be called to supply themismatch. In this example a combination of ESS 95 and conventionalreserves 94 are dispatched to achieve the lowest cost solution.Commitments 92 can be specified in blocks of arbitrary duration as shortas one minute and as long as various hours. Commitments in each timeblock can be flat, slope or otherwise shaped according to arbitrarymathematical models. Commitments can be continuous or discontinuousbetween adjacent blocks.

By way of example, FIG. 10 illustrates one method of shaping wind power101 into thirty-minute block commitments 102 where each block ischaracterized by slope 103. Adjacent blocks are allowed to bediscontinuous with jumps 104. By way of another example, FIG. 11illustrates alternative methods of shaping wind power into thirty-minuteblock commitments, where the block duration is purely exemplary. Panel111 illustrates wind shaping with maximum allowed slope of 1 MW/min andmaximum allowed jump of 100 MW. Panel 112 illustrates wind shaping withmaximum allowed slope of 1 MW/min and maximum allowed jump of 0 MW,which is equivalent to generating a continuous shape. Panel 113illustrates wind shaping with maximum allowed slope of 0 MW/min andmaximum allowed jump of 100 MW, which is equivalent to generating flatblock commitments. Panel 114 illustrates wind shaping with maximumallowed slope of 1 MW/min and maximum allowed jump of 0.3 MW. By way ofanother example, FIG. 12 illustrates a case where the slope of adjacentpower block commitments is made continuous by transition 121 and theslope reversal rate is constrained. This case is relevant, for example,when peaker power plants must track any variation in shaped output powerand their speed to transition from an upward ramp to a downward ramp orfrom a downward ramp to an upward ramp is limited.

An optimal embodiment of possible ESS operating strategies 17 for windshaping can implement the following algorithm:

-   -   a. Calculate optimal power block commitments based on renewable        resource forecast and constrained by user defined shape        requirements. These commitments are optimal by way of requiring        minimal additional reserves or ESS effort to fulfill any        deviation from average forecasted power;    -   b. Calculate difference between commitments and real-time        renewable generation;    -   c. Calculate combined ESS and reserves dispatch to minimize        balancing cost, subject to ESS and system constraints;    -   d. Calculate optimal ESS size and operating strategy;    -   e. Maximum and minimum capacity and other operational        constraints can be specified for the time horizon of ES        application and can be updated dynamically as a function of        external conditions as well as internal conditions (such as        outage of ESS hardware);    -   f. Many optimization strategies can be used to carry out the        calculations in (e.), including linear and non-linear        programming, as it will appear to those skilled in the art;    -   g. The algorithm can re-compute all quantities periodically and        possibly at each time step, in order to always enact the optimal        strategy.

The model can also consider the financial impact of the ESS operating inconjunction with balancing reserves, taking into account both thecapital cost and depreciation of assets and the recurring energy costs;and many other factors. For example, the actions of a battery can bemodulated by the cost of battery operation during the simulation becausethe financial worth of supplying balancing services may be less than theamortized cost of owning and operating the ESS, including wear anddepreciation of ESS hardware. Thus, the financial impact can operate asan integral component of ESS operation that is evaluated again at theend of a simulation to indicate the overall financial performance, whichcan be used for optimization and ultimately decision-making.

ES application optimization algorithm 12 can perform a series ofoptimization exercises to indicate the optimum ESS (in terms of powerand energy), an optimum operation of this ESS in conjunction with themicro-grid assets, and the financial results achieved (e.g., outputs 19in FIG. 8). This optimization can be based on balancing the total andmarginal costs of an ESS with the total and marginal revenues/costsavings realized through its operation, and in this way can take intoaccount the decreasing returns to scale of an ESS. The model can reflectbroad sets of exogenous assumptions and inputs, but has been structuredsuch that most of these can be varied to test and demonstrate ESSoperations and benefits under a wide range of conditions.

For example, the model can compute the ROT or other financial metric foreach of a set of strategies and ESS characteristics then choose the beststrategy and ESS characteristics to achieve the greatest ROI or otherfinancial metric. The optimum point can be located, for example, usinglist comparison, multivariate regression, local optimization techniquesthat travel up a local gradient vector, or other numerical optimizationmethod known to those skilled in the art.

An exemplary set of outputs 19 can be a graphical and numericalrepresentation of ESS performance, a list of financial metrics includingbut not limited to $USD, IRR, NPV, and those metrics as a function ofESS capacity, and the strategy used, including optimized strategyparameters.

FIG. 13 shows an exemplary embodiment of the graphical interface of therenewable energy balancing tool. Panel 131 controls shape requirementsfor block commitments; Panel 132 controls ESS size, life and economics;Panel 133 controls ESS feedback control strategy; Panel 134 controlsforecast uncertainty; Panel 135 sets the cost of conventional energy andpower reserves; Graph 136 shows granular renewable energy generation anddispatch of an ESS and reserves for balancing the mismatch of forecastand real-time; Graph 137 shows the statistical distribution of energybalancing requirements; Graph 138 shows the statistical distribution ofpower balancing requirements.

By way of another example, FIG. 14 illustrates an embodiment in a modelthat demonstrates a near-optimal charge and discharge schedule forenergy arbitrage with a model ESS. This model can also use the followingkey inputs, amongst others:

-   -   a. Historical LMP 13 at the node where power is bought and sold,        in intervals of one hour or less, over multi-mouth periods;    -   b. Power market models 14, including primary market drivers that        can affect power price dynamics and buy-sell decisions;    -   c. Power market rules and Constraints 15, conditioning the        ability to execute buy-sell trades;    -   d. Possible ESS configurations 16 relating to ESS capacity,        power rating, charge and discharge rates, useful life,        efficiency losses and other characteristics;    -   e. Possible ESS operating strategy 17 relating to the operating        strategy in conjunction with power markets so that most of the        value of power price volatility can be captured; and    -   f. ESS cost model 18 relating to a separate proprietary model,        and other relevant information, indicating the relative and        absolute cost of ESS's having different technologically feasible        characteristics e.g. with respect to power, energy, cycle life,        footprint, efficiency, etc.).

On the basis of the foregoing, the model can compare the amortized costof cycle life damage and round trip efficiency losses to the benefits ofeach potential energy “trade” such that unprofitable trades can beavoided. The low and high price points for purchase and sale of energy,respectively, can be identified from a large set with a novelpeak-trough locating algorithm (e.g., ES application possible ESSoperating strategies 17 in FIG. 14). By moving a window of comparisonthat causes pruning when local marginal price points are not localextrema or when the points do not make profitable trades, the algorithmcan prune intermediate value points and create a list of maximasatisfying the profitable trade criterion, as it will be apparent tothose skilled in the art.

FIG. 15 illustrates an embodiment of the peak-trough locating algorithm.Buy-sell pairs (blue dots 151) are identified and charge and dischargeorders 152 are scheduled. Subsequently, blue dots 151 are pruned fromthe set, which is left non-uniformly sampled (line 153). These buy-sellpairs can then be sequentially assigned as ESS charge and dischargeorders of magnitude equal to the ESS maximum power rating. Since the ESSmay have more energy available to use, multiple iterations can bepossible. Buy-sell pairs can be subsequently removed from the pricecurve and the process can be repeated multiple times to get other listsof actions. For an N hour ESS, N action layers can provide chargescheduling within ESS power and energy limits. Because the algorithmstated can allow rapid long-term optimization, an ESS can assess thevalue of energy storage independent of preset price points or othersituation-based inputs. Instead, it is capable of adapting to changes asthey appear in the forecast.

The model can also consider the financial impact of power arbitrageoperating in conjunction with the ESS, taking into account, for example,the financial worth of buy-sell trades; the capital cost,cycling-dependent ESS degradation, useful life and efficiency losses ofthe ESS; and many other factors. For example, the actions of a batterycan be modulated by the cost of battery operation during the simulationbecause the financial worth of buy-sell trades may be less than theamortized cost of owning and operating the ESS, including wear anddepreciation of ESS hardware. Thus, the financial impact can operate asan integral component of ESS operation that is evaluated again at theend of a simulation to indicate the overall financial performance, whichcan be used for optimization and ultimately decision-making.

ES application optimization algorithm 12 can perform a series ofoptimization exercises to indicate the optimum ESS (in terms of powerand energy), an optimum operation of this ESS in conjunction with powerarbitrage, and the financial results achieved (e.g., outputs 19 in FIG.14). This optimization can be based on balancing the total and marginalcosts of an ESS with the total and marginal revenues/cost savingsrealized through its operation, and in this way takes into account thedecreasing returns to scale of an ESS. The model can reflect broad setsof exogenous assumptions and inputs, but can be structured such thatmost of these can be varied to test and demonstrate ESS operations andbenefits under a wide range of conditions.

For example, the model can compute the ROI or other financial metric foreach of a set of strategies and ESS characteristics then choose the beststrategy and ESS characteristics to achieve the greatest ROI or otherfinancial metric. The optimum point can be located, for example, usinglist comparison, multivariate regression, local optimization techniquesthat travel up a local gradient vector, or other numerical optimizationmethod known to those skilled in the art.

An exemplary set of outputs 19 can be a graphical and numericalrepresentation of ESS performance, a list of financial metrics includingbut not limited to $USD, IRR, NPV, and those metrics as a function ofESS capacity, and the strategy used, including optimized strategyparameters

By way of another example, FIG. 16 illustrates an embodiment in a modelthat demonstrates the operation of an ESS installed for the purposes ofshaving peak loads. This embodiment can protect substation anddistribution transformers and can also help defer their upgrade. Thismodel can adopt the perspective of a substation transformer periodicallydriven above its rated power during periods of peak load. This model canalso use the following key inputs, amongst others:

-   -   a. Historical load 1613-1 at the transformer, in intervals of        one hour or less, over multi-month periods;    -   b. Historical ambient temperature 1613-2 at the transformer        location, in intervals of one hour or less;    -   c. Physical models of transformer 14, including the transformer        thermodynamic equations, calibrated with the transformer test        reports as well as any available records of the transformer        historical performance;    -   d. Pricing/penalty schemes for accelerated wear 15-1 aimed at        internalizing the costs incurred as a result of accelerated        depreciation and premature decommissioning as a consequence of        transformer overload;    -   e. Premium for transformer upgrade deferral 15-2 aimed at        capturing all incentives from deferring upgrade of the        transformer, for example the opportunity cost of capital        elsewhere invested;    -   f. Possible ESS configurations 16 relating to ESS capacity,        power rating, charge and discharge rates, useful life,        efficiency losses and other characteristics;    -   g. Possible ESS operating strategy 17 relating to the operating        strategy in conjunction with the transformer so that the        transformer is operated most of the time below its rated        maximum; and    -   h. ESS cost model 18 relating to a separate proprietary model,        and other relevant information, indicating the relative and        absolute cost of ESS's having different technologically feasible        characteristics (e.g. with respect to power, energy, cycle life,        footprint, efficiency, etc.).

On the basis of the foregoing, the model can solve the relevantthermodynamic equations to calculate transformer oil and windingstemperature in the most general conditions. This can be significantlymore accurate than the approximate set of equations advised in the IEEEC57.91-1995 standard and therefore can enable tighter margins ofoperation and fuller transformer capacity utilization.

An often referenced example of thermodynamic modeling of substationtransformers is G. Swift in IEEE TRANSACTIONS ON POWER DELIVERY, VOL.16, NO. 2, APRIL 2001. Accelerated aging as a function of temperaturecan be calculated according to the Arrhenius activation model adopted inthe same standard, or any other custom aging model, calibrated againsthistorical data, where available.

By way of example, FIG. 17 shows illustrative transformer load profile171 over 48-hour period characterized by five peaks 172 through 176 thatexceed transformer rated power 177. An optimal embodiment of possibleESS operating strategies 17 for transformer deferral can implement thefollowing algorithm:

-   -   a. Calculate accelerated wear of windings insulation for given        load and ambient temperature;    -   b. Quantify relative wear for each overload peak;    -   c. Identify periods of time when transformer is not overloaded        and ESS recharge is possible (Recharge Periods 178 and 179 in        FIG. 17);    -   d. Identify idle times when no ESS operation is permitted;    -   e. Calculate optimal allocation of available capacity to        mitigate overload peaks in such a way that minimizes transformer        wear, while respecting ESS operational constraints (such as        maximum and minimum capacity throughout the 48-hour period);    -   f. Maximum and minimum capacity and other operational        constraints can be specified for the time horizon of ES        application and can be updated dynamically as a function of        external conditions as well as internal conditions (such as        outage of ESS hardware);    -   g. Many optimization strategies can be used to carry out the        calculations in (e.), including linear and non-linear        programming, as it will appear to those skilled in the art;    -   h. The algorithm can re-compute all quantities periodically and        possibly at each time step, in order to always enact the optimal        strategy.

The model can also consider the financial impact of the transformeroperating in conjunction with the ESS, taking into account the economicimpact of unmitigated periodic overloads of the transformer as well asthe opportunity cost of deferring investment in a new transformer; thecapital cost, useful life and efficiency losses of the ESS; and manyother factors. For example, the actions of a battery can be modulated bythe cost of battery operation during the simulation because thefinancial worth of peak load shaving at the transformer may be less thanthe amortized cost of owning and operating the ESS, including wear anddepreciation of ESS hardware. Thus the financial impact can operate asan integral component of ESS operation that is evaluated again at theend of a simulation to indicate the overall financial performance, whichcan be used for optimization and ultimately decision-making.

ES application optimization algorithm 12 can perform a series ofoptimization exercises to indicate the optimum ESS (in terms of powerand energy), an optimum operation of this ESS in conjunction with thetransformer, and the financial results achieved (e.g., outputs 19 inFIG. 16). This optimization can be based on balancing the total andmarginal costs of an ESS with the total and marginal revenues/costsavings realized through its operation, and in this way takes intoaccount the decreasing returns to scale of an ESS. The model can reflectbroad sets of exogenous assumptions and inputs, but has been structuredsuch that most of these can be varied to test and demonstrate ESSoperations and benefits under a wide range of conditions.

For example, the model can compute the ROI or other combinations offinancial metrics for each of a set of strategies and ESScharacteristics then choose the best strategy and ESS characteristics toachieve the greatest ROI or other combinations of financial metrics. Theoptimum point can be located, for example, using list comparison,multivariate regression, Monte Carlo, local optimization techniques thattravel up a local gradient vector, or other numerical optimizationmethod known to those skilled in the art.

An exemplary set of outputs 19 can be a graphical and numericalrepresentation of ESS performance, a list of financial metrics includingbut not limited to $USD, IRR, NPV, and those metrics as a function ofESS capacity, and the strategy used, including optimized strategyparameters. The optimum point can be located, for example, using listcomparison, multivariate regression, local optimization techniques thattravel up a local gradient vector, or other numerical optimizationmethod known to those skilled the art.

FIG. 18 presents an exemplary basic operation of an ESS to shave loadpeaks at a substation transformer. Graph 181 illustrates the effect ofvarious batteries in mitigating sinusoidal peak of amplitude 5 MW: allbatteries were operated according to the optimal strategy of shaving theuppermost part of the peak to an extent compatible with the batterycapacity and power limits. Graph 182 illustrates the correspondingeffect in mitigating the temperature overrun of the hottest spot in thetransformer windings: an optimally operated, 1 5 MWh battery is able tolimit such effect to below 1 degree C., whereas the temperature wouldhave risen by approximately 8 degrees C. with no battery. In thisexample, the transformer had a rated power of 25 MVA and hot spottemperature at rated power of 110 degrees C. A 20% overload cantherefore determine a substantial increase in hot spot temperature;frequent overload can cause non-negligible wear of windings insulation.

FIG. 19 shows an exemplary embodiment of the graphical interface of thetransformer deferral optimization tool. Panel 191 sets out key inputsregarding specifications of the transformer, including (i) transformerrated power and losses, (ii) thermal masses and time constants ofinsulating mineral oil and transformer windings, and (iii) parameters tocalculate transformer degradation. A user can independently vary all ofthese inputs. Button 192 allows a user to import custom load andtemperature profiles.

Graph 193 contains a shape of transformer load, which is one input tothe model. Graph 194 contains a shape of ESS dispatch, which relates tothe shape of power supplied by the battery to augment generation andserve load. This could be generic and user defined. For example, batterydispatch can shave the very uppermost part of the load peak.Alternatively, battery dispatch can shave a front, a central or a backportion of the shape describing the load peak. In yet another example,battery dispatch could deliver constant power for the full or partialduration of the load peak; Graph 195 contains a shape of transformerwear caused by transformer load with and without ESS mitigation; Panel196 shows summary financial metrics from transformer deferralapplication.

Windings insulation wear can be calculated from the windings temperatureby means of the Arrhenius activation equation advised in the IEEEC57.91-1995 standard, which is customary for this application and iswell blown to those skilled in the art. By further integrating thewindings insulation wear function over the duration of the peak eventand comparing the same with the degree of wear had the temperaturestayed at the maximum transformer rated value, the excess wear withrespect to baseline can be calculated. The financial losses fromaccelerated wear of the transformer can be compared with the cost of theESS to assess the financial merits of this application.

The model can compute the aggregate financial metrics of subsequent usesof ESS at multiple sites. For example, an ESS can be designed to defer atransformer upgrade at a specific location for a number of years. Afterthis period has elapsed, the ESS can be moved to another location andsupport another transformer for a number of years. The benefits of bothapplications must then be accounted for in the valuation of ESSeconomics.

By way of another example, FIG. 20 illustrates an embodiment in a modelthat demonstrates the operation of an ESS installed for the purposes ofminimizing the energy cost of a micro-grid installation alsoincorporating renewable power, on-site fossil fuel generator and gridaccess. This embodiment can minimize the energy cost by one of twopossible strategies. If a power grid is present and able to supplyusers' power demand, an ESS can generate value by shaving peak load andavoiding peak demand charges, which also may relieve distributiontransformer overload, and by performing energy arbitrage betweenoff-peak and peak hours or between renewable energy in excess of loadand peak hours. If on the other hand, the micro-grid does not have gridaccess, an ESS can generate value by storing excess renewable energy anddisplacing fuel consumption and by optimizing the regime at which afossil fuel generator, or portfolio of other power sources, will run.For example, diesel generators are notoriously inefficient at low loadfractions. In such cases, the generator can be run at full capacity andany energy produced in excess of instantaneous load can be stored in thebattery for future use, resulting in a net gain in fuel efficiency, asit will be obvious to those skilled in the art. A portfolio of dieselgenerators will typically have different supply versus efficiencycharacteristic, in which case the strategy of portfolio management willbe coupled to ESS characteristics and usage algorithms. This model canadopt the perspective of a user trying to minimize its energy cost witha micro-grid type installation. This model can also use the followingkey inputs, amongst others:

-   -   a. Historical user's load 2013-1, typically in intervals of one        hour or less, over a desired time period;    -   b. Historical grid rates 2013-2, typically in intervals of one        hour or less;    -   c. Historical renewable energy generation 13-3, typically in        intervals of one hour or less;    -   d. Physical models 14-1 of ESS, including ESS rate of        degradation as a function of configuration and operating        parameters;    -   e. Physical models of on-site fossil fuel generator 14-2,        including fuel efficiency as a function of operating point and        rate of degradation over time;    -   f. Physical models of renewable generator 14-3, including rate        of degradation over time;    -   a. Physical models and usage costs of each generator in a        portfolio of generators;    -   g. Pricing schemes 15 for peak and off-peak energy rates, peak        demand charges and net-metering benefits that apply when excess        renewable energy is sold back to the grid;    -   h. Possible ESS configurations 16 relating to ESS capacity,        power rating, charge and discharge rates, useful life,        efficiency losses and other characteristics;    -   i. Possible ESS operating strategy 17 relating to the operating        strategy in conjunction with the other micro-grid assets so that        power absorbed from the grid is always kept below this user        defined threshold; and    -   j. ESS cost model 18 relating to a separate proprietary model,        and other relevant information, indicating the relative and        absolute cost of ESS's having different technologically feasible        characteristics (e.g. with respect to power, energy cycle life,        footprint, efficiency etc.).

On the basis of the foregoing, the model can calculate the lowest costdispatch of available resources to meet the user power demand, whilecomplying with the user's defined maximum grid absorption.

By way of example, FIG. 21 shows illustrative commercial user's loadprofile 211 over a weeklong period. The load can be served by acombination of grid energy 212, photovoltaic energy 213, battery 214 andon-site fossil fuel generator (e.g., 215, 217 as explained below), suchas diesel or fuel cell. An optimal embodiment of possible ESS operatingstrategies 17 for micro-grids can implement the following algorithm:

-   -   a. Calculate user's load net of renewable energy generator;    -   b. Impose user defined grid absorption limit;    -   c. Calculate battery dispatch to shave peak load and perform        energy arbitrage between off-peak and peak hours as well as        excess renewable energy generation and peak hours;    -   d. Dispatch on-site fossil generator to fulfill grid limit        constraint (215) as well as to achieve lowest energy cost during        peak hours (217);    -   e. Maximum and minimum capacity and other operational        constraints can be specified for the time horizon of ES        application and can be updated dynamically as a function of        external conditions as well as internal conditions (such as        outage of ESS hardware);    -   h. Operating strategies for the ESS can be updated depending on        changes in supply and demand of power sources.    -   f. Many optimization strategies can be used to carry out the        calculations in (e.), including linear and non-linear        programming, as it will appear to those skilled in the art;    -   g. The algorithm can re-compute all quantities periodically and        possibly at each time step, in order to always enact the optimal        strategy.

The model can also consider the financial impact of the micro-gridassets operating in conjunction with the ESS, taking into account boththe capital cost and depreciation of micro-grid assets and the recurringenergy costs; and many other factors. For example, the actions of abattery can be modulated by the cost of battery operation during thesimulation because the financial worth of peak load shaving may be lessthan the amortized cost of owning and operating the ESS, including wearand depreciation of ESS hardware. Thus, the financial impact can operateas an integral component of ESS operation that is evaluated again at theend of a simulation to indicate the overall financial performance, whichcan be used for optimization and ultimately decision-making.

ES application optimization algorithm 12 can perform a series ofoptimization exercises to indicate the optimum ESS (in terms of powerand energy), an optimum operation of this ESS in conjunction with themicro-grid assets, and the financial results achieved (e.g., outputs 19in FIG. 20). This optimization can be based on balancing the total andmarginal costs of an ESS with the total and marginal revenues/costsayings realized through its operation, and in this way takes intoaccount the decreasing returns to scale of an ESS. The model can reflectbroad sets of exogenous assumptions and inputs, but has been structuredsuch that most of these can be varied to test and demonstrate ESSoperations and benefits under a wide range of conditions.

For example, the model can compute the ROI or other combinations offinancial metrics for each of a set of strategies and ESScharacteristics then choose the best strategy and ESS characteristics toachieve the greatest ROI or other combinations of financial metrics. Theoptimum point can be located, for example, using list comparison,multivariate regression, local optimization techniques that travel up alocal gradient vector, or other numerical optimization method known tothose skilled in the art.

An exemplary set of outputs 19 can be a graphical and numericalrepresentation of ESS performance, a list of financial metrics includingbut not limited to $USD, IRR, NPV, and those metrics as a function ofESS capacity, and the strategy used, including optimized strategyparameters.

FIG. 22 shows an exemplary embodiment of the graphical interface of themicro-grid optimization tool. Panel 221 can control scaling of maximumand minimum load; Panel 222 can control scaling of energy rates, peakdemand charges and net metering payments; Panel 223 can control ESSsize, life and economics and entry 223-1 controls maximum gridabsorption; Panel 224 can control on-site fossil-fuel generator sizes,life and economics; Panel 225 can control renewable generator size, lifeand economics; Button 226 can import expected load profiles, renewableenergy generation and energy rates; Graph 227 shows granular dispatch ofmicro-grid assets; Graph 228 shows capital and operating costs broken byasset and comparison with cost benchmark for energy savings and paybackcalculation; Graph 229 shows a fossil-fuel generator efficiency curve;Graph 2210 shows a granular evolution of ESS state of charge; Graph 2211shows projected ESS degradation over time calculated from ESS physicalmodels.

In some embodiments in all of the interfaces shown, the user canindependently vary the inputs shown, whereupon the model can recalculateand present a revised set of graphs and calculations based on thechanged input. This recalculation process can be near instantaneous.

The aforementioned examples are just some of the methodology and toolsfor optimal planning of energy storage systems. In general, eachindividual ES application can simulate ESS performance and profitabilitybased on historical and forecast data and can therefore provide decisionmakers with an optimal estimate as of which ESS to deploy. Embodimentscan also run in real time and evaluate the financial benefits of servingeither one application in the foreseeable future, based on forecast dataproduced by state-of-the-art algorithms such as neural networks, baggeddecision trees and others, which are known to those skilled in the art.

ES applications can be subsequently ordered by financial worth and sizeof the opportunity, as illustratively shown in FIG. 23. In this example,dispatch stack 231 consists of four ES applications: (i) arbitrage A1,(ii) wind regulation WR, (iii) arbitrage A2, and (iv) transformerdeferral TD. For each ES application, embodiments of the systemdescribed herein can calculate the financial worth and the size of theopportunity with optimal ESS operation. For example, it was determinedthat ESS could capture financial opportunity FAI from arbitrage A1 withoptimal committed capacity CAI; likewise, ESS could capture financialopportunity FWR from wind regulation WR with optimal committed capacityCWR, financial opportunity FA2 from arbitrage A2 with optimal committedcapacity CA2 and financial opportunity FTD from transformer deferral TDwith optimal committed capacity CID. ES applications can be ordered bydescending financial worth, like illustratively shown in Dispatch stack231. ES applications can then be dispatched in order up to Available ESSCapacity 232, which can be smaller than the sum of the optimal committedcapacities of ES applications in the stack. This approach can providethe maximum financial returns from the available ESS capacity.

FIGS. 24A and B illustratively show one embodiment of real-timeoperation of an energy storage system. In an embodiment, the techniquesdescribed herein can be used to provide real-time control of the energystorage system using forecasted data, rather than historical data,though other data can be used. For example, a standard control systemcan receive forecasted data inputs, calculate the optimal operatingstrategy for an energy storage system, and then cause the energy storagesystem to operate in accord with the calculated optimal strategy. Thecontrol system can be configured such that it recalculates in real-timethe optimal operating strategy on a predefined interval, or as newforecast data are received.

ES application optimization tools 11-1 through 11-n-th, where n-th is ageneric number, can receive input from dedicated forecast tools 241-1through 241 n-th and compute in real-time the optimal financial worthand committed capacity for ES applications I through n-th. These resultscan then be sorted by real-time dispatch scheduler 242 in dispatch stack231, which can be dynamically updated in real-time. It should be notedthat other operational constraints can occasionally prevent a specificES application from being dispatched; alternatively, other operationalrequirements can lead to the dispatch of a specific ES application, evenif it is not the most profitable. Therefore, real-time dispatch stack231 can account for all these contingencies.

According to 231, controllers 243, 244 and 245 can respectively beallocated ESS capacities of generic names CAI, CA2, CWR and CTD (up toavailable ESS capacity 232) to dispatch in the time horizon ofcorresponding ES applications. These controllers can have significantdegree of intelligence in determining how to optimally dispatch theallocated capacity. Their real-time operation can also be fullyparameterized by allocated capacity as well as ESS operationalconstraints, so that they can always immediately adapt current dispatchstrategy to changing dispatch stack and other contingencies. AvailableESS capacity 232 can be constantly fed hack to real-time dispatchscheduler 242 via feedback link 247. In this specific example, it isassumed that arbitrage applications A1 and A2 can be fulfilled by thesame controller, however this does not need to be the case.

Real-time controllers can enact any optimal ESS operating strategies,including, but not limited to, the ones illustrated in FIG. 4, FIG. 9,FIG. 15, FIG. 18 and FIG. 21. By way of example, an optimal controllerfor transformer deferral can implement the following algorithm:

-   -   a. Calculate accelerated wear of windings insulation for given        forecast load and ambient temperature;    -   b. Quantify relative wear for each overload peak;    -   c. Identify periods of time when transformer is not overloaded        and ESS recharge is possible (Recharge Periods 178 and 179 in        FIG. 17);    -   d. Identify idle times when no ESS operation is permitted;    -   e. Calculate optimal allocation of available capacity to        mitigate overload peaks in such a way that minimizes transformer        wear, while respecting ESS operational constraints (such as        maximum and minimum capacity throughout the 48-hour period);    -   f. Maximum and minimum capacity and other operational        constraints can be specified for the time horizon of an ES        application and can be updated dynamically as a function of        external conditions (such as the capacity allocated by Real Time        Dispatch Scheduler 232) as well as internal conditions (such as        outage of ESS hardware);    -   g. Many optimization strategies can be used to carry out the        calculations in (e.), including linear and non-linear        programming, as it will appear to those skilled in the art;    -   h. The algorithm can re-compute all quantities periodically and        possibly at each time step, in order to always enact the optimal        strategy.

For the purpose of this description, it should be noted that the ESSavailable capacity does not need to be embodied in a single physicaldevice. Distributed deployment, where applicable, can provide additionalbenefits because it enables more granular power and energy services,such as protection of neighborhood transformers or assistance withelectric vehicle charging stations. FIG. 25 illustratively shows theequivalence of ESS 246 and a network of ESS 252, in communication andcoordination via distributed energy storage (DES) Gateway 251. Likewise,each of ESS 252 can be a network of subunits, each one of which canadopt ES application prioritization processes and dispatch stack. Thus,embodiments can apply to each level of a multi-layer ESS infrastructurein a way that maximizes global as well as local performance metrics suchprofitability, reliability, accessibility, etc.

The subject matter described herein can be implemented in digitalelectronic circuitry, or in computer software, firmware, or hardware,including the structural means disclosed in this specification andstructural equivalents thereof, or in combinations of them. The subjectmatter described herein can be implemented as one or more computerprogram products, such as one or more computer programs tangiblyembodied in a non-transitory information carrier (e.g., in a machinereadable storage device), or embodied in a propagated signal, forexecution by, or to control the operation of data processing apparatus(e.g., a programmable processor, a computer, or multiple computers). Acomputer program (also known as a program, software, softwareapplication, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, and it can bedeployed in any form, including as a stand-alone program or as a module,component, subroutine, or other unit suitable for use in a computingenvironment. A computer program does not necessarily correspond to afile. A program can be stored in a portion of a file that holds otherprograms or data, in a single file dedicated to the program in question,or in multiple coordinated files (e.g., files that store one or moremodules, sub programs, or portions of code). A computer program can bedeployed to be executed on one computer or on multiple computers at onesite or distributed across multiple sites and interconnected by acommunication network.

The processes and logic flows described in this specification, includingthe method steps of the subject matter described herein, can beperformed by one or more programmable processors executing one or morecomputer programs to perform functions of the subject matter describedherein by operating on input data and generating output. The processesand logic flows can also be performed by, and apparatus of the subjectmatter described herein can be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processor of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read only memory ora random access memory or both. The essential elements of a computer area processor for executing instructions and one or more memory devicesfor storing instructions and data. Generally, a computer will alsoinclude, or be operatively coupled to receive data from or transfer datato, or both, one or more mass storage devices for storing data, e.g.,magnetic, magneto optical disks, or optical disks. Information carrierssuitable for embodying computer program instructions and data includeall forms of non-volatile memory, including by way of examplesemiconductor memory devices, (e.g., erasable programmable read-onlymemory (EPROM), electrically erasable programmable read-only memory(EEPROM), and flash memory devices); magnetic disks, (e.g., internalhard disks or removable disks); magneto optical disks; and optical disks(e.g., compact discs (CDs) and digital versatile discs (DVDs)). Theprocessor and the memory can be supplemented by, or incorporated in,special purpose logic circuitry.

To provide for interaction with a user, the subject matter describedherein can be implemented on a computer having a display device, e.g., aCRT (cathode ray tube) or LCD (liquid crystal display) monitor, fordisplaying information to the user and a keyboard and a pointing device,(e.g., a mouse or a trackball), or a touchscreen, by which the user canprovide input to the computer. Other kinds of devices can be used toprovide for interaction with a user as well. For example, feedbackprovided to the user can be any form of sensory feedback, (e.g., visualfeedback, auditory feedback, or tactile feedback), and input from theuser can be received in any form, including acoustic, speech, or tactileinput.

The subject matter described herein can be implemented in a computingsystem that includes a back end component (e.g., a data server), amiddleware component (e.g., an application server), or a front endcomponent (e.g., a client computer having a graphical user interface ora web browser through which a user can interact with an implementationof the subject matter described herein), or any combination of such backend, middleware, and front end components. The components of the systemcan be interconnected by any form or medium of digital datacommunication, e.g., a communication network. Examples of communicationnetworks include a local area network (“LAN”) and a wide area network(“WAN”), e.g., the Internet.

The foregoing has been a detailed description of illustrativeembodiments of the invention. Various modifications and additions can bemade without departing from the spirit and scope of this invention. Eachof the various embodiments described above may be combined with otherdescribed embodiments in order to provide multiple features.Furthermore, while the foregoing describes a number of separateembodiments of the methodology and tools of the present invention, whathas been described herein is merely illustrative of the application ofthe principles of the present invention. For example, the appearance,the features, the inputs and outputs and the mathematical algorithms ofcomponents described herein can be varied to suit a particularapplication. Accordingly, this description is meant to be taken only byway of example, and not to otherwise limit the scope of this invention.

To the extent certain functionality or components “can” or “may” beperformed or included, respectively, the identified functionality orcomponents are not necessarily required in all embodiments and can beomitted from certain embodiments of the invention.

To the extent that the foregoing description refers to the “invention,”the present disclosure may include more than one invention.

1. A method, for energy storage asset management, the method comprising:providing input data including energy pricing data, energy incentivedata, energy storage system configuration data, and an energy storagesystem cost model; determining, based on the input data, an optimalallocation of energy storage capacity to each energy-related applicationfrom a plurality of energy-related applications of an energy storagesystem; and causing the energy storage system to perform multiple energystorage (ES) applications in an application stack with an energy storageasset of the energy storage system based on the determined optimalallocation of energy storage capacity.
 2. The method of claim 1, whereinthe energy pricing data includes a pricing scheme for peak energy rates.3. The method of claim 1, wherein the energy pricing data includes apricing scheme for off-peak energy rates.
 4. The method of claim 1,wherein the energy pricing data includes a pricing scheme for peakdemand charges.
 5. The method of claim 1, wherein the energy incentivedata includes data associated with a net-metering benefit that isapplicable when excess renewable energy is sold back to the power grid.6. The method of claim 1, wherein the energy storage systemconfiguration data includes one of: a capacity, a power rating, a chargerate, a discharge rate, a useful life, or an efficiency loss of theenergy storage system.
 7. The method of claim 1, further comprisingupdating the optimal allocation of energy storage capacity in responseto a data forecast.
 8. The method of claim 1, wherein the input datafurther includes a weather forecast.
 9. A method, comprising: receiving,at a compute device, input data including: energy pricing data, energyincentive data, indications of a plurality of energy storage systemconfigurations, indications of a plurality of operating strategies foran energy storage system, and a cost model for the energy storagesystem; identifying, via the compute device, an optimal operatingstrategy from the plurality of operating strategies for the energystorage system based on the input data; and causing the energy storagesystem to perform multiple energy storage (ES) applications in anapplication stack with an energy storage asset of the energy storagesystem, using a controller operably coupled to the compute device, andbased on the identified optimal operating strategy for the energystorage system.
 10. The method of claim 9, wherein the energy pricingdata includes at least one of: a pricing scheme for peak energy rates, apricing scheme for off-peak energy rates, or peak demand charges. 11.The method of claim 9, wherein the energy incentive data includes dataassociated with a net-metering benefit that is applicable when excessrenewable energy is sold back to the power grid.
 12. The method of claim9, wherein at least one operating strategy from the plurality ofoperating strategies is an operating strategy that maximizes anoperating life of the energy storage system.
 13. The method of claim 9,wherein at least one operating strategy from the plurality of operatingstrategies is an operating strategy that maximizes an economic value ofthe energy storage system.
 14. The method of claim 9, wherein theidentified optimal operating strategy is the operating strategy from theplurality of operating strategies that is associated with a lowest costdispatch of available resources to meet a user power demand whilecomplying with a user-defined constraint.
 15. The method of claim 9,wherein each energy storage system configuration from the plurality ofenergy storage system configurations includes at least one of: capacityinformation, power rating information, charge rate information,discharge rate information, efficiency loss information, or useful lifeinformation.
 16. The method of claim 9, wherein the identifying theoptimal operating strategy from the plurality of operating strategies isperformed using at least one of: list comparison, multivariateregression, local optimization, linear programming, non-linearprogramming, a Monte Carlo optimization, machine learning, regressionfitting, or multivariate optimization.
 17. The method of claim 9,wherein the input data further includes one of historic energyproduction data or a physical model of an ES application from themultiple ES applications.
 18. The method of claim 9, wherein the optimaloperating strategy is a first optimal operating strategy, the methodfurther comprising: receiving, via an interface of the compute device, amodification to the input data; and identifying, via the compute device,a second optimal operating strategy from the plurality of operatingstrategies based on the modification to the input data.
 19. The methodof claim 9, further comprising updating the optimal allocation of energystorage capacity in response to one of an external condition or aninternal condition.
 20. The method of claim 9, wherein the input datafurther includes a weather forecast.